A machine includes a bronze cart sliding horizontally on steel rails. The design is changed to add a 15° angle to the rails and cart without changing any other features. How does the sliding friction of the two designs compare?

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Friction occurs because of the interatomic forces at these minute regions of atomic contact. The fraction of the geometric area in atomic contact is proportional to the normal force divided by the geometric area. If the normal force is doubled, the area of atomic contact is doubled and the friction is twice as large. However, if the geometric area is doubled while the normal force remains the same, the fraction of area in atomic contact is halved and the actual area in atomic contact hence the friction force remains constant.